The invention provides a block member and a panel structure which are of a relatively simple construction, which may permit reduction in production and fabrication costs, which may be easily assembled with a sufficient strength, and which may have superior appearance when assembled. A block member comprises a block body 21 of a rectangular configuration having a center point and four sides, the block body including a flange portion 24 in the outer peripheral surface 21c of each of the four sides, the flange portions being formed integrally with the block body and protruding outwardly from the outer peripheral surface, the flange portions having a thickness less than that of the outer peripheral surface, each of the flange portions having a deformed portion 25 which restricts the amount of protrusion of the flange portion 24, the deformed portions being formed in the flange portions disposed at corner portions of the block body at which the adjoining sides of the block body meet together. The block members are clamped by the pair of support members disposed along the front and rear surface of the flange portions 24, through the use of a space defined by the deformed portions 25 and attachment holes in the support members.